Question

Factorise the expression and divide as directed

Answer 1

Answer:

(i) y^2+7y+10\ =\ y^2+2y+5y+10y  

2

+7y+10 = y  

2

+2y+5y+10

=\ y\ \left(y+2\right)+5\left(y+2\right)= y (y+2)+5(y+2)

=\ \left(y+5\right)\left(y+2\right)= (y+5)(y+2)

Division: \frac{\left(y+5\right)\left(y+2\right)}{y+5}=\ y+2  

y+5

(y+5)(y+2)

​  

= y+2

(ii) m^2-14m-32\ =\ m^2-16m+2m-32m  

2

−14m−32 = m  

2

−16m+2m−32

=\ m\left(m-16\right)+2\left(m-16\right)= m(m−16)+2(m−16)

=\ \left(m+2\right)\left(m-16\right)= (m+2)(m−16)

Division: \frac{\left(m+2\right)\left(m-16\right)}{m+2}  

m+2

(m+2)(m−16)

​  

 

= m-16

(iii) 5p^2-25p+20\ =\ 5\left(p^2-5p+4\right)5p  

2

−25p+20 = 5(p  

2

−5p+4)

= 5\left(p^2-4p-p+4\right)5(p  

2

−4p−p+4)

=5\left[p\left(p-4\right)-1\left(p-4\right)\right]5[p(p−4)−1(p−4)]

=5\left(p-1\right)\left(p-4\right)5(p−1)(p−4)

Division: \frac{5\left(p-1\right)\left(p-4\right)}{p-1}  

p−1

5(p−1)(p−4)

​